Wood Roof Tie (LRFD, NDS 2018)

How it calculates

Rafter geometry and horizontal thrust

The calculator resolves the pitched rafter geometry from the horizontal span and roof pitch. For a rafter spanning from the ridge to the wall plate, the horizontal outward thrust at the wall plate that the tie must resist is derived from the tributary load and pitch angle:

H = (w × L / 2) / tan(θ)

where w is the total factored load per unit length of the rafter (dead plus live or snow under the governing ASCE 7 LRFD combination), L is the horizontal rafter span, and θ is the pitch angle. For a collar tie positioned at height y above the wall plate, the tie tension is amplified by the ratio of the full rafter height h to the tie height y:

Pu = H × (h / y)

Tie tension check

The factored tensile resistance of the tie member per NDS 2018 LRFD:

φTn = φ_t × K_F,t × F_t × λ × C_M × C_t × C_F × A_n

where φ_t = 0.80 for tension parallel to grain, K_F,t is the format conversion factor, λ is the time-effect factor for the governing load combination (0.8 for occupancy live, 1.15 for roof live or snow, 1.0 for wind), and A_n is the net cross-sectional area at connections. The utilization ratio Pu / φTn must be ≤ 1.0.

Rafter bending and shear checks

The rafter is modeled as a simply supported inclined member loaded by self-weight and the applied gravity load. The governing factored bending moment Mu occurs at or near mid-span, and the critical shear Vu is taken at the face of the support.

φMn = φ_b × K_F,b × F_b × λ × C_M × C_t × C_F × C_r × C_L × S

φVn = φ_v × K_F,v × F_v × λ × C_M × C_t × (2/3 × A)

where φ_b = 0.85 for bending and φ_v = 0.75 for shear. The beam stability factor C_L is computed from the slenderness ratio R_B based on the lateral bracing condition of the rafter. Both Mu / φMn and Vu / φVn must be ≤ 1.0.

Deflection check

Rafter mid-span deflection under serviceability load combinations is computed using beam bending theory for the inclined span. The calculator checks against a user-specified span-to-deflection ratio (default L/240 for total load). Long-term deflection includes the NDS creep multiplier for the sustained dead load component.

Time-effect factor and LRFD adjustment factors

All resistance values are adjusted by the time-effect factor λ, which parallels the ASD load duration factor C_D. For the governing load combination, λ takes values of 0.6 for permanent dead load only, 0.8 for occupancy live, 1.15 for roof live or snow, and 1.0 for wind. The calculator automatically selects the governing combination and applies the corresponding λ to each capacity term, along with the format conversion factor K_F and the applicable wet service, temperature, and size factors.